The present invention relates generally to magnetic resonance imaging, and more specifically, to a system and method for designing multi-dimensional spatially-selective RF pulse profiles using an optimal control approach. By defining an RF pulse profile using optimal control, the resulting magnetization therefrom can be rendered more accurately, especially for larger tip angles. Embodiments of the present invention find particular utility in parallel transmission applications such as localized magnetization manipulations, and in B1 inhomogeneity correction at high main magnetic field strengths. However, one skilled in the art will appreciate that improved RF pulse profiles will benefit any MR imaging process.
MR imaging in general is based upon the principle of nuclear magnetic resonance. When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field, such as a B1 excitation field, which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, or “longitudinal magnetization”, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins after the excitation signal B1 is terminated and this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals is digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
For systems using multiple coils or multi-channel RF pulses, as well as for sequences which utilize multidimensional spatially-selective RF pulses, it is beneficial for the RF pulses transmitted by the coils to produce accurate changes in magnetization. In conventional single channel transmission, multidimensional pulses to achieve multidimensional spatial selectivity can have much longer durations than the single dimensional slice-selective pulses. The performance of the single channel transmission pulses can also be rather limited. Thus, parallel transmission of independently-controlled multidimensional RF waveforms has been used to shorten the transmission times and improve the performance of spatial selectivity. However, to date, parallel transmission has only been used for certain types of RF pulses, since most design methods for parallel transmission pulses are based upon mere approximations of the Bloch equations, and therefore are accurate only when certain limitations are met.
One common RF pulse design approach is known as the small tip angle (STA) approximation, which is generally accurate for RF pulse profiles having tip angles of less than 90 degrees. Another approach is known as the linear class large tip angle approximation (LCLTA). These approaches are limited in that they are mere linear approximation of the Bloch equations, and thus have inherent errors in their results. These errors can be translated into ripples and rounded edges in the magnetization profiles when the assumptions of STA/LCLTA are approximately met, or into large distortions from the ideal magnetization profiles when the assumptions are violated. As such, it has been thought that these types of pulses should be derived directly from the Bloch equations.
However, direct derivation of RF pulse shapes from the Bloch equations has so far been limited in practice to single dimensional, single channel (i.e. non-parallel) RF pulses. Some of the more common approaches to directly solving the Bloch equations for 1D single channel pulses are the well-known Shinnar-LeRoux method, the utilization of neural networks, evolutionary methods, simulated annealing, perturbation response methods, iterative correction for hardware non-linearity, optimal control, inverse scattering transforms, and others. Unfortunately, none of these methods have so far been generalized to accommodate RF pulse design for multi-channel pulse waveforms and/or multi-dimensional spatially-selective pulse waveforms.
It would therefore be desirable to have a system and method capable of producing accurate multidimensional and/or multichannel RF pulse waveforms. It would be further desirable to have embodiments of such a system and method which could account for arbitrary desired flip angles and arbitrary initial magnetization.